Regression between true scores
Hiroshi Watanabe · Japanese Psychological Research · 1984
Our model presented in this paper is such that, given pairs of observed first test and second test scores, each observed score is expressed by a sum of true score and error score where the relationship between the pairs of true scores are strictly linear. The linear relationship implied under this model is much less strong than the essential τ-equivalence relationship. By employing this model and the split-half technique, it is shown that the estimates of the true regression coefficients and the reliability coefficients of the two tests are obtainable from nine equations. Furthermore, the results show that the absolute value of the estimated true slope is larger than or equal to the absolute value of the ordinary least squares estimate of slope, and the observed correlation coefficient between the two tests is the geometric mean of the estimated reliability coefficients for the two tests.